Space is the boundless three-dimensional extent in which
objects and events have relative position and direction.[1] Physical space is often conceived in three
lineardimensions, although modern
physicists usually consider it, with
time, to be part of a boundless four-dimensional
continuum known as
spacetime. The concept of space is considered to be of fundamental importance to an understanding of the physical
universe. However, disagreement continues between philosophers over whether it is itself an entity, a relationship between entities, or part of a
conceptual framework.

Debates concerning the nature, essence and the mode of existence of space date back to antiquity; namely, to treatises like the Timaeus of
Plato, or
Socrates in his reflections on what the Greeks called khôra (i.e. "space"), or in the Physics of
Aristotle (Book IV, Delta) in the definition of topos (i.e. place), or in the later "geometrical conception of place" as "space qua extension" in the Discourse on Place (Qawl fi al-Makan) of the 11th-century Arab polymath
Alhazen.[2] Many of these classical philosophical questions were discussed in the
Renaissance and then reformulated in the 17th century, particularly during the early development of
classical mechanics. In
Isaac Newton's view, space was absolute—in the sense that it existed permanently and independently of whether there was any matter in the space.[3] Other
natural philosophers, notably
Gottfried Leibniz, thought instead that space was in fact a collection of relations between objects, given by their
distance and
direction from one another. In the 18th century, the philosopher and theologian
George Berkeley attempted to refute the "visibility of spatial depth" in his Essay Towards a New Theory of Vision. Later, the
metaphysicianImmanuel Kant said that the concepts of space and time are not empirical ones derived from experiences of the outside world—they are elements of an already given systematic framework that humans possess and use to structure all experiences. Kant referred to the experience of "space" in his Critique of Pure Reason as being a subjective "pure a priori form of intuition".

Philosophy of space

Galilei

Galilean and
Cartesian theories about space, matter and motion are at the foundation of the
Scientific Revolution, which is understood to have culminated with the publication of
Newton's Principia in 1687.[5] Newton's theories about space and time helped him explain the movement of objects. While his theory of space is considered the most influential in Physics, it emerged from his predecessors' ideas about the same.[6]

As one of the pioneers of
modern science, Galilei revised the established
Aristotelian and
Ptolemaic ideas about a
geocentric cosmos. He backed the
Copernican theory that the universe was
heliocentric, with a stationary sun at the center and the planets—including the Earth—revolving around the sun. If the Earth moved, the Aristotelian belief that its natural tendency was to remain at rest was in question. Galilei wanted to prove instead that the sun moved around its axis, that motion was as natural to an object as the state of rest. In other words, for Galilei, celestial bodies, including the Earth, were naturally inclined to move in circles. This view displaced another Aristotelian idea—that all objects gravitated towards their designated natural place-of-belonging.[7]

René Descartes

Descartes set out to replace the Aristotelian worldview with a theory about space and motion as determined by
natural laws. In other words, he sought a
metaphysical foundation or a
mechanical explanation for his theories about matter and motion.
Cartesian space was
Euclidean in structure—infinite, uniform and flat.[8] It was defined as that which contained matter; conversely, matter by definition had a spatial extension so that there was no such thing as empty space.[5]

The Cartesian notion of space is closely linked to his theories about the nature of the body, mind and matter. He is famously known for his "cogito ergo sum" (I think therefore I am), or the idea that we can only be certain of the fact that we can doubt, and therefore think and therefore exist. His theories belong to the
rationalist tradition, which attributes knowledge about the world to our ability to think rather than to our experiences, as the
empiricists believe.[9] He posited a clear distinction between the body and mind, which is referred to as the
Cartesian dualism.

Leibniz and Newton

Following Galilei and Descartes, during the seventeenth century the
philosophy of space and time revolved around the ideas of
Gottfried Leibniz, a German philosopher-mathematician, and
Isaac Newton, who set out two opposing theories of what space is. Rather than being an entity that independently exists over and above other matter, Leibniz held that space is no more than the collection of spatial relations between objects in the world: "space is that which results from places taken together".[10] Unoccupied regions are those that could have objects in them, and thus spatial relations with other places. For Leibniz, then, space was an idealised
abstraction from the relations between individual entities or their possible locations and therefore could not be
continuous but must be
discrete.[11]
Space could be thought of in a similar way to the relations between family members. Although people in the family are related to one another, the relations do not exist independently of the people.[12]
Leibniz argued that space could not exist independently of objects in the world because that implies a difference between two universes exactly alike except for the location of the material world in each universe. But since there would be no observational way of telling these universes apart then, according to the
identity of indiscernibles, there would be no real difference between them. According to the
principle of sufficient reason, any theory of space that implied that there could be these two possible universes must therefore be wrong.[13]

Newton took space to be more than relations between material objects and based his position on
observation and experimentation. For a
relationist there can be no real difference between
inertial motion, in which the object travels with constant
velocity, and
non-inertial motion, in which the velocity changes with time, since all spatial measurements are relative to other objects and their motions. But Newton argued that since non-inertial motion generates
forces, it must be absolute.[14] He used the example of
water in a spinning bucket to demonstrate his argument. Water in a
bucket is hung from a rope and set to spin, starts with a flat surface. After a while, as the bucket continues to spin, the surface of the water becomes concave. If the bucket's spinning is stopped then the surface of the water remains concave as it continues to spin. The concave surface is therefore apparently not the result of relative motion between the bucket and the water.[15] Instead, Newton argued, it must be a result of non-inertial motion relative to space itself. For several centuries the bucket argument was considered decisive in showing that space must exist independently of matter.

Kant

In the eighteenth century the German philosopher
Immanuel Kant developed a theory of
knowledge in which knowledge about space can be both a priori and synthetic.[16] According to Kant, knowledge about space is synthetic, in that statements about space are not simply true by virtue of the meaning of the words in the statement. In his work, Kant rejected the view that space must be either a substance or relation. Instead he came to the conclusion that space and time are not discovered by humans to be objective features of the world, but imposed by us as part of a framework for organizing experience.[17]

Non-Euclidean geometry

Euclid's Elements contained five postulates that form the basis for Euclidean geometry. One of these, the
parallel postulate, has been the subject of debate among mathematicians for many centuries. It states that on any
plane on which there is a straight line L1 and a point P not on L1, there is exactly one straight line L2 on the plane that passes through the point P and is parallel to the straight line L1. Until the 19th century, few doubted the truth of the postulate; instead debate centered over whether it was necessary as an axiom, or whether it was a theory that could be derived from the other axioms.[18] Around 1830 though, the Hungarian
János Bolyai and the Russian
Nikolai Ivanovich Lobachevsky separately published treatises on a type of geometry that does not include the parallel postulate, called
hyperbolic geometry. In this geometry, an
infinite number of parallel lines pass through the point P. Consequently, the sum of angles in a triangle is less than 180° and the ratio of a
circle's
circumference to its
diameter is greater than
pi. In the 1850s,
Bernhard Riemann developed an equivalent theory of
elliptical geometry, in which no parallel lines pass through P. In this geometry, triangles have more than 180° and circles have a ratio of circumference-to-diameter that is less than
pi.

Type of geometry

Number of parallels

Sum of angles in a triangle

Ratio of circumference to diameter of circle

Measure of curvature

Hyperbolic

Infinite

< 180°

> π

< 0

Euclidean

1

180°

π

0

Elliptical

0

> 180°

< π

> 0

Gauss and Poincaré

Although there was a prevailing Kantian consensus at the time, once non-Euclidean geometries had been formalised, some began to wonder whether or not physical space is curved.
Carl Friedrich Gauss, a German mathematician, was the first to consider an empirical investigation of the geometrical structure of space. He thought of making a test of the sum of the angles of an enormous stellar triangle, and there are reports that he actually carried out a test, on a small scale, by
triangulating mountain tops in Germany.[19]

Henri Poincaré, a French mathematician and physicist of the late 19th century, introduced an important insight in which he attempted to demonstrate the futility of any attempt to discover which geometry applies to space by experiment.[20] He considered the predicament that would face scientists if they were confined to the surface of an imaginary large sphere with particular properties, known as a
sphere-world. In this world, the temperature is taken to vary in such a way that all objects expand and contract in similar proportions in different places on the sphere. With a suitable falloff in temperature, if the scientists try to use measuring rods to determine the sum of the angles in a triangle, they can be deceived into thinking that they inhabit a plane, rather than a spherical surface.[21] In fact, the scientists cannot in principle determine whether they inhabit a plane or sphere and, Poincaré argued, the same is true for the debate over whether real space is Euclidean or not. For him, which geometry was used to describe space was a matter of
convention.[22] Since
Euclidean geometry is simpler than non-Euclidean geometry, he assumed the former would always be used to describe the 'true' geometry of the world.[23]

Einstein

In 1905,
Albert Einstein published his
special theory of relativity, which led to the concept that space and time can be viewed as a single construct known as spacetime. In this theory, the
speed of light in a
vacuum is the same for all observers—which has
the result that two events that appear simultaneous to one particular observer will not be simultaneous to another observer if the observers are moving with respect to one another. Moreover, an observer will measure a moving clock to
tick more slowly than one that is stationary with respect to them; and objects are measured
to be shortened in the direction that they are moving with respect to the observer.

Subsequently, Einstein worked on a
general theory of relativity, which is a theory of how
gravity interacts with spacetime. Instead of viewing gravity as a
force field acting in spacetime, Einstein suggested that it modifies the geometric structure of spacetime itself.[24] According to the general theory, time
goes more slowly at places with lower gravitational potentials and rays of light bend in the presence of a gravitational field. Scientists have studied the behaviour of
binary pulsars, confirming the predictions of Einstein's theories, and non-Euclidean geometry is usually used to describe spacetime.

Mathematics

In modern mathematics
spaces are defined as
sets with some added structure. They are frequently described as different types of
manifolds, which are spaces that locally approximate to Euclidean space, and where the properties are defined largely on local connectedness of points that lie on the manifold. There are however, many diverse mathematical objects that are called spaces. For example,
vector spaces such as
function spaces may have infinite numbers of independent dimensions and a notion of distance very different from Euclidean space, and
topological spaces replace the concept of distance with a more abstract idea of nearness.

Space is one of the few
fundamental quantities in
physics, meaning that it cannot be defined via other quantities because nothing more fundamental is known at the present. On the other hand, it can be related to other fundamental quantities. Thus, similar to other fundamental quantities (like time and
mass), space can be explored via
measurement and experiment.

Relativity

Before
Einstein's work on relativistic physics, time and space were viewed as independent dimensions. Einstein's discoveries showed that due to relativity of motion our space and time can be mathematically combined into one object–
spacetime. It turns out that distances in
space or in
time separately are not invariant with respect to Lorentz coordinate transformations, but distances in Minkowski space-time along
space-time intervals are—which justifies the name.

In addition, time and space dimensions should not be viewed as exactly equivalent in Minkowski space-time. One can freely move in space but not in time. Thus, time and space coordinates are treated differently both in
special relativity (where time is sometimes considered an
imaginary coordinate) and in
general relativity (where different signs are assigned to time and space components of
spacetimemetric).

Cosmology

Relativity theory leads to the
cosmological question of what shape the universe is, and where space came from. It appears that space was created in the
Big Bang, 13.8 billion years ago[28] and has been expanding ever since. The overall shape of space is not known, but space is known to be expanding very rapidly due to the
cosmic inflation.

Spatial measurement

The measurement of physical space has long been important. Although earlier societies had developed measuring systems, the
International System of Units, (SI), is now the most common system of units used in the measuring of space, and is almost universally used.

Geographical space

Geography is the branch of science concerned with identifying and describing places on
Earth, utilizing spatial awareness to try to understand why things exist in specific locations.
Cartography is the mapping of spaces to allow better navigation, for visualization purposes and to act as a locational device.
Geostatistics apply statistical concepts to collected spatial data of Earth to create an estimate for unobserved phenomena.

Geographical space is often considered as land, and can have a relation to
ownership usage (in which space is seen as
property or territory). While some cultures assert the rights of the individual in terms of ownership, other cultures will identify with a communal approach to land ownership, while still other cultures such as
Australian Aboriginals, rather than asserting ownership rights to land, invert the relationship and consider that they are in fact owned by the land.
Spatial planning is a method of regulating the use of space at land-level, with decisions made at regional, national and international levels. Space can also impact on human and cultural behavior, being an important factor in architecture, where it will impact on the design of buildings and structures, and on farming.

Ownership of space is not restricted to land. Ownership of
airspace and of
waters is decided internationally. Other forms of ownership have been recently asserted to other spaces—for example to the radio bands of the
electromagnetic spectrum or to
cyberspace.

Public space is a term used to define areas of land as collectively owned by the community, and managed in their name by delegated bodies; such spaces are open to all, while
private property is the land culturally owned by an individual or company, for their own use and pleasure.

Abstract space is a term used in
geography to refer to a hypothetical space characterized by complete homogeneity. When modeling activity or behavior, it is a conceptual tool used to limit
extraneous variables such as terrain.

In psychology

Psychologists first began to study the way space is perceived in the middle of the 19th century. Those now concerned with such studies regard it as a distinct branch of
psychology. Psychologists analyzing the perception of space are concerned with how recognition of an object's physical appearance or its interactions are perceived, see, for example,
visual space.

In the Social Sciences

Space has been studied in the social sciences from the perspectives of
Marxism,
feminism,
postmodernism,
postcolonialism,
urban theory and
critical geography. These theories account for the effect of the history of colonialism, transatlantic slavery and globalization on our understanding and experience of space and place. The topic has garnered attention since the 1980s, after the publication of
Henri Lefebvre's The Production of Space . In this book, Lefebvre applies Marxist ideas about the production of commodities and accumulation of capital to discuss space as a social product. His focus is on the multiple and overlapping social processes that produce space.[29]

In his book The Condition of Postmodernity,David Harvey describes what he terms the "
time-space compression." This is the effect of technological advances and capitalism on our perception of time, space and distance.[30] Changes in the modes of production and consumption of capital affect and are affected by developments in transportation and technology. These advances create relationships across time and space, new markets and groups of wealthy elites in urban centers, all of which annihilate distances and affect our perception of linearity and distance.[31]

In his book Thirdspace,Edward Soja describes space and spatiality as an integral and neglected aspect of what he calls the "
trialectics of being," the three modes that determine how we inhabit, experience and understand the world. He argues that critical theories in the Humanities and Social Sciences study the historical and social dimensions of our lived experience, neglecting the spatial dimension.[32] He builds on Henri Lefebvre's work to address the dualistic way in which humans understand space—as either material/physical or as represented/imagined. Lefebvre's "lived space"[33] and Soja's "thridspace" are terms that account for the complex ways in which humans understand and navigate place, which "firstspace" and "Secondspace" (Soja's terms for material and imagined spaces respectively) do not fully encompass.

Postcolonial theorist
Homi Bhabha's concept of
Third Space is different from Soja's Thirdspace, even though both terms offer a way to think outside the terms of a
binary logic. Bhabha's Third Space is the space in which hybrid cultural forms and identities exist. In his theories, the term
hybrid describes new cultural forms that emerge through the interaction between colonizer and colonized.[34]

References

^Refer to Plato's Timaeus in the Loeb Classical Library,
Harvard University, and to his reflections on khora. See also Aristotle's Physics, Book IV, Chapter 5, on the definition of topos. Concerning Ibn al-Haytham's 11th century conception of "geometrical place" as "spatial extension", which is akin to
Descartes' and Leibniz's 17th century notions of extensio and analysis situs, and his own mathematical refutation of Aristotle's definition of topos in natural philosophy, refer to:
Nader El-Bizri, "In Defence of the Sovereignty of Philosophy: al-Baghdadi's Critique of Ibn al-Haytham's Geometrisation of Place", Arabic Sciences and Philosophy (
Cambridge University Press), Vol. 17 (2007), pp. 57–80.